Conventional methods and systems for interrogating a material or medium are generally based on linear interaction of acoustic waves with the material or medium. Some methods and techniques in the geophysics community have been implemented to study non-linear interaction of acoustic waves in a rock formation but each has its own limitations. The time reversal technique involving the propagation backward in time of a wavefield scattered by linear interaction in a medium has also been used to focus the wavefield back onto a point in the medium that acts as a micro-seismic source.
Therefore, there remains a need for methods and systems for investigating non-linear properties of materials that provide enhanced multi-dimensional image information of non-linear properties of the material or medium using non-linear acoustic interactions in the medium to emulate micro-seismic sources originating from locations of the non-linear interaction in the medium.